Without any exceptions, all of the existing versions of the Coriolis force flowmeter or the convective inertia force flowmeter employ a combination of one or a pair of conduits under a flexural vibration and two vibration sensors respectively detecting the flexural vibration of the conduit at two different sections of the conduit, wherein the mass flow rate of fluid media moving through the conduit is determined as a product of a constant and a function of a phase angle difference (or other variable related to the phase angle difference). In the present day practice, the numerical value of the above-mentioned constant of proportionality relating the phase angle difference to the mass flow rate of media is determined by calibrating the flowmeter, which numerical value or the product of the numerical value and the frequency of the flexural vibration of the conduit is then treated as a constant number in the operation of the flowmeter. As to be shown by the description of the operating principles of the present invention, the above-mentioned constant of proportionality is not a physical constant, but it is a physical variable having a numerical value that is a function of the dynamic parameters characterizing the flexural vibration of the conduit filled with fluid. By flexurally vibrating the conduit filled with the fluid media at a natural frequency thereof in the operation of the flowmeter, the numerical value of the above-mentioned constant of proportionality can be kept at a constant value as long as the dynamic parameters of the vibrating system such as the amplitude and frequency of the flexural vibration, density of the fluid media, bending stiffness of the conduit, etc. do not experience a significant change due to the changing working environment and varying property of the fluid media. Otherwise, the existing versions of the Coriolis force flowmeters fail to measure the mass flow rate of fluid media with an accuracy meeting the standard set by the calibration of the flowmeter. It will become clear as the derivation and description of the operating principles of the present invention progresses that the existing versions of the Coriolis force flowmeters are operated on a theoretical foundation satisfying the principles of dynamics in a less than rigorous manner and, consequently, they lack the self-calibrating ability required to maintain the accuracy in the mass flow measurement at the level set by the initial calibration of the flowmeter independent of the changing conditions in the property of fluid media and the working environment. Another short-coming of the existing versions of the Coriolis force flowmeters is their vulnerability to ambient mechanical vibrations and their inability to measure the mass flow rate of media having low values of density such as gaseous media, which short-coming results from the fact that, in the present day practice of the operation of the convective inertia force or Coriolis force flowmeter, the convective inertia force experienced by the media and providing the measure of mass flow rate of the media is measured by measuring the effect thereof on the flexural vibration of the conduit (the phase angle difference between the flexural vibrations of two opposite halves of the conduit) rather than measuring directly the convective inertia force experienced by the fluid media. The present invention teaches a new method for measuring directly the convective inertia force experienced by the fluid media and determining the mass flow rate of fluid media from the directly measured value of the convective inertia force experienced by the fluid media, and provides a new inertia force mass flowmeter calibrating itself on a real time basis and capable of measuring mass flow rate of liquid media as well as gaseous media, which new inertia force mass flowmeter can be constructed in all sizes varying from a very small size to a very large size.